Kabakov’s focus during those years was his albums, specifically, a series that relates, through images and text, the stories of 10 absurdist figures, such as “the Flying Komarov,” a man who looks through his window to see a whirlwind of citizens flying in the skies above Moscow. By the early 1980s, Kabakov had begun conceiving environments in which such fictional personages might reside, but it was not until he left the repressive confines of Moscow for the more laissez-faire international stage that he was able to show these pieces in museums and galleries.

Like Kabakov’s albums, the installations—which incorporate paintings, many of them by the artist himself, as well as pastiches of Soviet graphic art, explanatory texts and everyday objects—have a literary quality that evokes the Russian novel more than Western conceptual art. The first of these works that he showed, in 1988, was the groundbreaking “10 Characters,” for which he transformed New York’s Ronald Feldman Gallery into a communal apartment subdivided into living areas for 10 fictional personages similar to those developed in his graphic albums. The most famous of his imaginary tenants is “the man who flew into space from his apartment,” whose room is dominated by a hammocklike contraption that apparently allowed him to catapult himself out of his cramped quarters. Many critics interpreted it as a potent metaphor for the fantasy of escaping the Soviet regime.

Another of the apartment’s inmates is the “man who never threw anything away,” an allusion to Kabakov himself. While living in Moscow, he created pieces from refuse he’d accumulated in his studio, the now-legendary space at 6/1 Sretensky Boulevard that he occupied for some 20 years, starting in 1967. In her monograph on the Kabakovs, the art critic Amei Wallach describes it as “an artist’s garret out of La bohème,” with “eaves so sloping it was often necessary to bend.”

The couple’s Mattituck studio, a ground-floor space they added to the house, is well ordered and rubbish free. Awash in pale light that floods through north-facing windows, it is “not so big, but big enough for my biggest paintings,” says Ilya. On one wall hangs a large canvas in progress, while on a nearby tabletop sits a wooden model about the size of a dollhouse. Emilia says that this simple chapel-like structure is meant to hold a group of paintings—a glance inside reveals miniature canvases pasted to the walls—and that they hope to build it someday.

Across the lawn from the studio, a separate structure that serves as a kind of minimuseum houses numerous such models for projects, both realized and unrealized. The replicas are all presented on wooden bases and enclosed in Plexiglas cases. Walking along the narrow aisles between the models, Emilia explains in detail the project each represents. One replica is for The Ship of Siwa, 2006, a sailboat stitched together from drawings made by children in Siwa, Egypt. Another is for Red Wagon, the full-size version of which is in the Moscow retrospective, a walk-in metaphor for three phases of Russian art history: Visitors climb a Constructivist staircase to a drably painted Soviet-era train car inside which idealized Socialist Realist landscapes are displayed to the accompaniment of nationalistic music. They exit from the train into an area scattered with garbage that represents unofficial art from the 1960s to the collapse of the Soviet Union in the 1980s.

The Kabakovs have shifted in their recent work to more general utopian themes and say they intend to balance pieces that, like Red Wagon, explicitly evoke the Soviet past with others that address broader issues. “When people think ‘Kabakov,’ they think ‘toilet,’ or ‘communal apartment,’ ” says Emilia. “They think everything is about Soviet Russia. But it’s not. It’s also about culture, about philosophy, about literature, about the history of art.”

Emblematic of the last concern is the ongoing series “An Alternative History of Art,” begun in 1997. The paintings, actually done by Ilya, are attributed to fictional artists representing three generations: Charles Rosenthal, who is supposed to have died in 1933, the year of his creator’s birth; Ilya Kabakov, the artist’s alter ego; and Igor Spivak, whose paintings are dated to the 1990s. In the studio, Emilia discourses on a few of the canvases from the series. One is a Rosenthal, depicting a naturalistically rendered scene of young people reading, on which are superimposed abstract, Malevich-like white squares, the whole representing an attempt to reconcile tradition with the avant-garde. She also points to a painting by Spivak, whose palette of whites and chalky reds, she explains, betrays his nostalgia for Soviet times. He paints “with rose-colored glasses on,” she says.